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Tangent to a curve intersects the y-axis at a point P . A line perpendicular to this tangent through P passes through the point 1 , 0 . The differential equation of the curve is

Options

  1. Ay d y d x - x d y d x 2 = 1
  2. Bx d 2 y d x 2 + d y d x 2 = 1
  3. Cy d x d y + x = 1
  4. DNone of these

Correct answer

A. y d y d x - x d y d x 2 = 1

Step-by-step solution

Equation of tangent at the point R x , f x is, Y − f x = f ′ x X − x Coordinates of the point are P ( 0 , f x - x f ′ x ) The slope of the perpendicular line through P is f x - x f ′ x - 1 = - 1 f ′ x y d y d x - x d y d x 2 = 1 is the differential equation.

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